Difference between revisions of "2022 SSMO Team Round Problems/Problem 14"
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The game works as follows: | The game works as follows: | ||
| + | * If a piggie drops a water balloon from any floor of the building, it will either break, or it will survive the fall. | ||
| + | * If the water balloon breaks, then any greater fall would have broken it as well. | ||
| + | * If the water balloon survives, then it would have survived any lesser fall. | ||
| + | * Every water balloon is identical and interchangeable. | ||
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The goal for the piggies is to find the lowest floor that will break a water balloon. Assuming they play optimally, what is the minimum number of tries in which they are guaranteed to find the lowest balloon-breaking floor? | The goal for the piggies is to find the lowest floor that will break a water balloon. Assuming they play optimally, what is the minimum number of tries in which they are guaranteed to find the lowest balloon-breaking floor? | ||
==Solution== | ==Solution== | ||
Latest revision as of 13:08, 14 December 2023
Problem
On a hot summer day, three little piggies decide to play with water balloons. The three piggies travel to a 200-floor parking garage each armed with exactly one water balloon.
The game works as follows:
- If a piggie drops a water balloon from any floor of the building, it will either break, or it will survive the fall.
- If the water balloon breaks, then any greater fall would have broken it as well.
- If the water balloon survives, then it would have survived any lesser fall.
- Every water balloon is identical and interchangeable.
The goal for the piggies is to find the lowest floor that will break a water balloon. Assuming they play optimally, what is the minimum number of tries in which they are guaranteed to find the lowest balloon-breaking floor?
